The formula for \(\bar{Q}\)  in Eq. REF  is efficient to compute when \(d> kr\) , as the most expensive step is inverting a \(kr\times kr\)  matrix that does not grow with \(d\) . Computing the matrix product from left to right also avoids storing a potentially large \(d\times d\)  matrix in memory. However, if feature maps are large or the shot number is particularly high (\(kr> d\) ), Eq. REF  may quickly become infeasible to compute. In this case an alternative formulation for \(\bar{Q}\)  exists, which swaps \(d\)  for \(kr\)  in terms of computational requirements. This formulation is owed to the Woodbury Identity [1]} as applied in [2]}:
\(\bar{Q}_c = \rho \bar{W}S_c = \rho Q(S_c^TS_c+\lambda I)^{-1}S_c^TS_c\) 
